After I took a Linear Algebra class I often found many Linear Algebra results that weren't covered in the class. I would like to learn these results therefore I am looking for a book, or even Notes written in Latex, that need to satisfy the following characteristics :
Covering topics on linear algebra that are generally not covered in basic linear algebra courses, in particular matrix decomposition formulas like the polar decomposition, the Schur decomposition and the Jordan Canonical form. I would also like to learn about the Gershgorin cirle theorems, matrix norms and their inequalities (for example the Hadamard inequality), and any "interesting" theorem about matrices, for example the fact that complex diagonalizable matrices are dense.
The book need to not focus on numerical methods, I want to learn these topics in order to use them when i need to, maybe for proving a statement, definitely not to solve a linear system by numerical methods.
It's preferable that the book doesn't spend too much time talking about "basic stuff" like the definition of a vector space, of a matrix etc. This is because I already took a course in Linear Algebra so I already know these topics
I would like the book to have advanced exercises, definitely not basic exercises like "compute this vector in this base". I would like the exercises to allow you to deepen the theory, basically like the exercises in Baby Rudin book
